Prism

A
prism
is a three-dimensional figure or
polyhedron
having two faces (called the bases of the prism) which are congruent polygons, and the remaining faces
parallelograms
.

If the remaining faces are rectangles (as in the figure
2
nd
figure above), then the prism is called a
right prism
. School level math books usually only talk about right prisms, and sometimes when they say prism they mean right prism.

A
triangular prism
is a prism with a triangular base, like the figure on the right. A
rectangular prism
is a prism with a rectangular base. (The cube is a special case.) Similarly, a prism with a
5
-sided base is a
pentagonal prism
, a prism with a
6
-sided base is a
hexagonal prism
, etc.

Volume of a Prism

The volume
V
of a right prism is given by the formula

V
=
B
h
,

where
B
is the area of the base and
h
is the height.

Example:

Find the volume of the prism shown.

The height of the prism is
10
cm. The base is a right triangle with legs of length
5
cm and
12
cm, so

B
=
1
2
(
5
)
(
12
)
=
1
2
(
60
)
=
30
cm
2

Therefore, the volume is

V
=
B
h
=
30
(
10
)
=
300
cm
3

Note that for a rectangular prism, the volume formula becomes simply

V
=
l
w
h
,

where
l
is the length of the base,
w
is the width of the base, and
h
is the height of the prism.

Surface Area of a Prism

The surface area
S
of a prism is given by the formula

S
=
2
B
+
P
h
,

where
B
is the area of the base of the prism,
P
is the
perimeter
of the base, and
h
is the height.